2 Answers
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A black hole (briefly), is nothing more than a dead star whose mass was more than 3 solar masses. When that star's life ended it collapsed under its own gravity and went through a supernova, losing a portion of its original gas in the process, thus losing part of its mass, and thus its total gravitational pull is diminished compared to the original star (contrary to common believe for a black hole having the "ultimate gravity"). So first of all, black holes vary in size and are not all the same (thing).

If we say the original star was orbiting around another star (A Binary system), (putting other factors aside) the effect on the other star from the black hole's gravitational forces would be less compared to its original star.

However that gravitational pull increases drastically as you go closer to the blackhole, since all the remaining matter is concentrated into a single point (singularity). Gravity becomes too severe, close to a blackhole that even light can not escape, an area called "the event horizon" of the black hole. But that's too close to the black hole. Nothing is special about its gravitational effect on the further objects as I pointed out with the orbiting star.

Regarding your statement: "Is it true also for objects like black holes? Are they even able to be moved by another force?" I don't know what you mean to be moved by another force, but black holes do move as any other object in space, they are nothing more than the remainder of their original star, and they inherited its motion relative to the other objects around. If say the original star was rotating around the center of it's galaxy, it will continue to do so.

Your statement: "bodies with low gravity force orbit around another one with higher gravity force" is not very accurate, since (bodies with higher gravity force - the more massive object), and (bodies with low gravity force - lesser mass) both orbit one another.

For instance, as the Moon orbits the Earth, the Earth also orbits the Moon, they both orbit around a point between the two of them called the "Barycenter". This point is always closer to the more massive object.

In the case of the Earth-Moon system it's inside the Earth's volume. Therefore it's common believe that only the Moon's orbiting the Earth, without the other way around as well.

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